Z 3 2 ρq 2 w 1 z 3 1 z 2 2 q 2 gw 2 z 2 2 z 3 2 1 z

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z 3 2 ) = ρ∙Q 2 w ( 1 z 3 1 z 2 ) 2 Q 2 g∙W 2 = ( z 2 2 z 3 2 ) ( 1 z 3 1 z 2 ) 2 Q 2 g∙W 2 = ( z 2 z 3 ) ( z 2 + z 3 ) ( z 2 z 3 z 3 ∙ z 2 ) 2 Q 2 g∙W 2 = ( z 3 ∙ z 2 )( z 2 + z 3 ) (17) (18) (19) (20) (21)
z 2 ∙ z 3 2 + z 2 2 ∙ z 3 2 Q 2 g∙W 2 = 0 Total Head In situations where pressure is expressed as a height it is called head. The prime example of this is the static head is the static pressure divided by the density times gravity. The lab manual gives the total head equation as: H tot = P ρ∙ g + 1 2 v 2 g + z Change in Total Head Across the Hydraulic Jump For this experiment, the change in total head across the hydraulic jump can calculated by the change in the total head between point 2 and 3 in the stream. Therefore, the total head difference is: ∆ H = H 3 H 2 = ( P 3 ρ∙g + 1 2 v 3 2 g + z 3 ) ( P 2 ρ∙g + 1 2 v 2 T 2 g + z 2 ) Both P 1 and P 2 are P atm , and v 2 is the theoretical as well as v3 calculated using the continuity equation [9]: Q 2 = Q 3 A 2 ∙ v 2 T = A 3 ∙v 3 v 3 = z 2 ∙v 2 T z 3 Therefore, simplify equation [23] to: ∆ H = H 3 H 2 = ( 1 2 ( z 2 ∙v 2 T z 3 ) 2 g + z 3 ) ( 1 2 v 2 T 2 g + z 2 ) (22) (23) (24) (25)
Experimental Procedure The procedure used was one that was handed out in the Fluid Mechanics 1 Laboratory Manual 1 . There was no deviation from this procedure and refer to figure 1 below for a higher understanding of the flow to be studied and the control volume of the hydraulic jump. Figure 1: Schematic of the flow to be studied and the control volume of the hydraulic pump.
Results and Discussion Table 3: Summary of Results Results Flow 1 Flow 2 Error Flow 1 Error Flow 2 V1 Theoretical 0.78997763 0.847198881 35.60% 46.04% V1 Measured 0.508740177 0.45715374 V2 Theoretical 6.846472789 7.855844169 35.60% 46.04% V2 Measured 4.409081537 4.239061951 V3 1.621533029 2.009634555 Q 0.215287184 0.252982213 z3 Theoretical 0.564875886 0.593141454 29.93% 24.48% z3 Measured 0.395833333 0.447916667 change in H theory 0.247624114 0.469358546 68.27% 28.72% change in H measure 0.416666667 0.604166667 Total Head 1 34.74754566 34.99677133 Total Head 2 34.32688082 34.32486412 Total Head 3 34.36771857 34.44170253 When applying Bernoulli’s equation across the sluice gate we find that the velocity is 6.8465 ft/s for the first flow test. For the second flow test the velocity was found to be 7.8558 ft/s. This makes sense because the flow for test two was higher than for test one. Using the flow rate equation the velocities for flow one and flow two are respectively, 4.4091 ft/s and 4.2391 ft/s at point two. These values do not make sense because the flow should have been faster in the second case. This would be caused by incorrect reading of the pitot tube or the tube not being placed parallel with the stream. The velocity upstream of the gate was found using the continuity equation using the velocities found at point two. The velocity at point one for flow one was 0.78998 ft/s and was 0.8472 ft/s for flow two using the theoretical velocities. Using the measured velocities at point two we find the velocities at point one are 0.5087 ft/s for flow one and 0.4572 ft/s for flow two. These values do not make sense for the same reason that the measured velocities at point two do not make sense. v 1 and v 2 have a significant error of 35.6% which could have come from friction along the channel and from the transfer at the sluice gate. This could

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